Talk
Stability of persistent homolgy
Abstract
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In this mini-course, we introduce persistent homology of a continuous function on a topological space. We define two descriptors, called the persistence Betti numbers functions and persistence diagrams and study the relations between them. In particular, we show that they are equivalent topological descriptions of the function and that one can be recovered from the other. We conclude by showing that persistent homology is a stable descriptor of a continuous function with respect to the uniform norm.
Keywords
Persistence diagram, persistence Betti numbers function, bottleneck distance
Prerequisites
Basic notions of linear algebra and calculus are enough. Knowing the definition of homology may also help.
Audience
The target audience is math undergraduate students. But anyone who would like to see more details on the main objects in Topological Data Analysis is also welcome.
Language
English
